Existing methods for skin lesion classification in non-stationary environments often fail to address the challenges of concept drift and data imbalance. This leads to catastrophic forgetting and reduced performance on minority classes. Traditional approaches typically rely on static models, which struggle to adapt to non-stationary and imbalanced data distributions, especially where concept drift occurs. This results in biased predictions and poor generalization, particularly for minority classes. To address these issues, Continual Learning for Skin Lesion Classification (CLSL) is proposed in this paper. CLSL introduces a novel combined loss function that assigns higher weights to hard-to-classify samples and incorporates a class margin adjustment mechanism. It enhances the model’s ability to identify minority classes. Additionally, CLSL employs a multi-classifiers system with dynamic weight assignment and weighted averaging of classification results to mitigate catastrophic forgetting. Wrongly classified samples are selectively retrained. This enables the model to adapt to new data while preserving knowledge from previous tasks. The method proposed in this paper contributes to partially solves the fairness problem in machine learning. Experimental results show that CLSL outperforms state-of-the-art methods in non-stationary and imbalanced data environments. It achieves superior accuracy and robustness in skin lesion classification tasks.